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Imagine I have a device that can stop time for the person who holds it (similar to Bernard's Watch). This device works in a very specific way - it creates a bubble around the user (just large enough to hold the user) in which time flows much faster than in the rest of the universe. The difference is very high but it is finite (say 100,000 times faster). This means that if the person holding the device experience times at "normal speed" the rest of the world outside the bubble appears to him to be drastically slowed down, almost (but not quite) to a standstill. In contrast, anyone outside the bubble looking in would see everything inside the bubble happening at lightning fast speed (almost instantaneously).

The border between this bubble of faster time and the rest of the universe is not infinitely thin - there is a boundary (say a few centimetres thick) where the speed of time changes gradually from one to the other.

My question is what side effects would this bubble cause? For example: any sounds from the outside would sound quieter and deeper, as the wavelengths are "stretched out" at the boundary. Similarly looking out of the bubble the outside world would appear darker and redder, as light is red-shifted. In fact with enough time dilation you would be able to see x-rays with your naked eyes. I'm also positing that waves such as light and sound would also bend at the boundary, as if they had struck a lense, so the outside world would appear distorted. Moving object such as bullets would also be deflected slightly (if they struck at an angle).

Are there any other interesting effects that could arise? What would happen if you walked up to another person, as they crossed the bubble's boundary? Is there anything cool you could do with this device?

For extra credit: would this violate any physically laws in any way e.g. conservation of energy? Show your working!

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    $\begingroup$ +1 for catching all of the typical mistakes people make with time stopping! $\endgroup$ – Cort Ammon Oct 9 '16 at 18:45
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    $\begingroup$ Wouldn't that make the guy inside die pretty quickly? $\endgroup$ – LiquidMetal Oct 9 '16 at 20:37
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    $\begingroup$ In Brandon Sanderson's Mistborn books, one of the magical powers available to Allomancers is the creation of speed bubbles similar to the ones described here. The author originally wanted to have the bubbles cause a realistic redshift effect, but he dropped the idea after a bit of research showed that it would end up essentially microwaving the people inside. This actually gets lampshaded in one of the books, when a researcher focused on the interactions between magic and physics mentions wondering why speed bubbles don't cause redshift. $\endgroup$ – Mason Wheeler Oct 10 '16 at 13:46
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    $\begingroup$ @LiquidMetal - The guy would only "die pretty quickly" according to your external frame of reference. The person/people inside the bubble would still experience their full natural life of 76.2 years (on average). Based on the OP's "100,000 times faster" supposition, if the person in the bubble needs 10 years to complete a task, people outside the bubble would see him complete the task in .0001 years (or a little less than a hour). But yes, people outside the bubble could witness a baby grow old and die by the end of their workday. $\endgroup$ – Tim Oct 10 '16 at 16:23
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    $\begingroup$ @LiquidMetal The rain would be very light inside the bubble. If there are 100000 raindrops/second outside the bubble then inside there will be 1 raindrop/second. $\endgroup$ – immibis Oct 11 '16 at 7:31
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As you point out, the world outside the bubble will appear darker - much darker. What appears as visible light is actually very, very far infrared (about 0.1 meter wavelength) and the energy available is virtually nil at these wavelengths.

Interface effects make this a superb weapon of assassination. Simply walk up to the victim and position yourself so that only part of his body is within the bubble. The portion inside will have "normal" metabolism, but if the heart is outside the bubble there will be no circulation and the tissue will die in minutes. Simply stand in place for a half-hour subjective, then move on. The effects of massive tissue death will be enormously traumatic for the victim.

Alternatively, stand aside from the victim and point a flashlight at where you you believe him to be, and hold it there for a while. Let's say you have a 10 watt beam, and you hold it for 30 minutes. The result (outside the bubble) will be an 18 kJ (10 watts x 60 x 30 seconds) pulse of extreme gamma radiation directed at the target.

Of course, you'll need SCUBA tanks or something similar, since you'll use up the oxygen in your bubble fairly quickly (subjectively). You'll also need to come up with a method of heat management. On the one hand, you are effectively encased in a black body at 0 K which will suck the heat out of you and leave you frozen solid. If, on the other hand, you posit that the interface characteristics are normally reflective (so you don't freeze) then not only can you not use the flashlight, the longer you operate your bubble the hotter you'll get, since resting human metabolism is about 100 watts, and this has nowhere to go.

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    $\begingroup$ Ooh good points on oxygen and heat management, I hadn't thought of that. You might not even need a torch, your own body heat could be shifted to lethal gamma if the rate was high enough! $\endgroup$ – Drgabble Oct 9 '16 at 18:43
  • $\begingroup$ @Drgabble - Yes, but it's onmidirectional, so not very selective - and not as intense as a flashlight. $\endgroup$ – WhatRoughBeast Oct 9 '16 at 19:06
  • $\begingroup$ Good point... on another note, running the numbers, for a bubble of 1.5m radius I'm calculating just over a days worth of oxygen, so it's not too bad on the breathing front $\endgroup$ – Drgabble Oct 9 '16 at 19:16
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    $\begingroup$ @Drgabble - You need to worry about CO2 buildup more than oxygen depletion. CO2 gets toxic pretty quickly - suppresses respiratation. $\endgroup$ – WhatRoughBeast Oct 9 '16 at 19:30
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    $\begingroup$ I feel like the oxygen and CO2 problem would only be an issue if you aren't moving around. Since things can enter and leave the bubble, you just need to be sure to move further than the diameter of the bubble every x minutes where x is the amount of time for the oxygen or CO2 effects to become dangerous. You'd also need to remember that moving back into the same space as you previously were in the same time trip will have you back at a place that is low in oxygen and high in CO2. $\endgroup$ – Shufflepants Oct 10 '16 at 2:32
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Well, let's see how such a field would work. The Hamiltonian equations are $$\frac{\mathrm d x_k}{\mathrm d t} = \frac{\partial H}{\partial p_k} \quad \frac{\mathrm d p_k}{\mathrm d t} = -\frac{\partial H}{\partial x_k}$$ Now we want the field to affect the speed of things happening, so a natural assumption would be that the field just acts as factor of the Hamiltonian: $$H(x,p) = \exp(f(x,t)) H_0(x,p)$$ Here the exponential function mainly is there to make time go normally when the field is zero. It however also makes sure time cannot go reverse.

Now for a constant non-zero field, you'd just get a rate of temporal change proportional to $\exp(f)$, so if the field is positive, things are going faster, as intended.

However what happens in the "bubble wall", assuming a static field? Well, here we have to use the product rule: \begin{aligned} \frac{\mathrm d x_k}{\mathrm d t} &= \exp{f(x)}\frac{\partial H_0}{\partial p_k}\\ \frac{\mathrm d p_k}{\mathrm d t} &= -\exp(f(x))\frac{\partial H_0}{\partial x_k} - f'(x)\exp(f(x))H_0(x,p) \end{aligned} Note the extra term on the second equation. This is an extra force proportional to the derivative of the field and the total Hamiltonian (which more or less gives the total energy). Assuming that energy is positive, this means that this acts like an extra repulsive force. Note that this repulsive force is in addition to the slowing down due to the local factor, and its strength depends on how rapidly the field grows. Note that since the kinetic energy is proportional to the mass, this leads also to a force term proportional to mass, similar to gravitation. Any potential energy would, however, give rise to an extra force that is not mass dependent.

Let's look at the energy, now also with time-dependent field: $$\frac{\mathrm dE}{dt} = \frac{\partial H}{\partial t} = \exp(f(x,t))\frac{\partial H}{\partial t} + \frac{\partial f}{\partial t}\exp(f(x,t))H_0(x,p)$$ So energy change only happens with field change, and proportional to it; that can well be explained as energy going into the field (of which I only included the effect). As long as the field remains constant, energy is conserved.

In effect, the outside world would look colder than would be expected from the slowdown, as the additional force would draw away more energy from incoming particles;on the other hand, outgoing particles would get an extra boost, so to the outside world, you'd be hotter than expected from the speedup.

Indeed, with a sufficiently small border zone (and corresponding rapid onset of the field) the border might even act like a wall for all normal-speed particles coming from outside.

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  • $\begingroup$ Fascinating. So this "repulsive force" would be proportional to the boundary width? Is it possible to get a formula for that? And with a thin enough boundary you could block radiation and material from passing through? $\endgroup$ – Drgabble Oct 9 '16 at 19:25
  • $\begingroup$ Actually it would be proprtional to the field change. But the thinner the boundary, the steeper the field change must be to achieve the same field value (it's not different to a hill: If the hill has a steep slope, you'll have a shorter, but harder way to the top). $\endgroup$ – celtschk Oct 9 '16 at 19:29
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In Larry Niven’s 1975 story, there were several side effects of note, used as clues by the detective to figure out that this was used. Besides the logistics of needing food, water, and medicine for an extended time relative to the outside world, the user had to sit in the dark because the flashlight inside the bubble became a powerful weapon seen from outside and set the wallpaper on fire (and presented as a novel unknown weapon to the M.E.).

Stasis fields were a staple of Niven’s work during that period, so read the Known Space universe and others written during the some years for more ideas.

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  • $\begingroup$ Sorry can I just check that's the right link? Doesn't seem to mention that... $\endgroup$ – Drgabble Oct 9 '16 at 18:34
  • $\begingroup$ You’ll have to read the novella. The time-slowing bubble is revealed at the end, but there are clues throughout. $\endgroup$ – JDługosz Oct 9 '16 at 18:36
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    $\begingroup$ If I remember right, the one with the time-slowing field is ARM (the locked-room mystery one, where the inventor of the time-field was killed and a flashlight is a possible murder weapon). Defenseless Dead comes first and focuses on the ethics of organ transplants. $\endgroup$ – Draconis Oct 10 '16 at 4:58
  • $\begingroup$ +1 for Niven though. The story also brings up the issue in WhatRoughBeast's answer: someone reaches into the field for (to them) a few seconds, and the time difference cuts off blood flow to their arm for (effectively) hours. The damage is bad enough that they have to amputate. $\endgroup$ – Draconis Oct 10 '16 at 5:02
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    $\begingroup$ @Draconis the whole body transplant (noted in the Wikipedia page) made me think that this was for healing time (which I remember was the point). Maybe I'm getting them mixed up though. The arm for a few seconds also killed the villian who was grabbed until he died of thirst. $\endgroup$ – JDługosz Oct 10 '16 at 10:00
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There is one effect that is derived directly from special relativity. It is remarkably surprising no-one has noticed it. This is based on the fact that the speed of light will always be constant in all frames of reference.

If time inside the 'quick-time' bubble is passing 100,00 times than in the outside world, and since the speed of light must be constant inside the bubble, then lengths in the bubble must increase by a factor of 100,000. This is the inverse of the Lorentz-FitzGerald length contraction. Effectively this is a length expansion.

For example, if the 'quick-time' bubble has a diameter of two metres in its frame of reference, then due to length expansion its size will have expanded out to two hundred kilometres in the frame of reference of the outside world.

This suggests someone inside a 'quick-time' bubble can't sneak into art galleries and museums to steal their treasures. As, for example, in Arthur C Clarke's SF short story "All the Time in the World". Any fast-moving giant can be easily detected and just as easily stopped with a few flashlights.

Of course, the Flash would have the same problem. What a pity. I rather liked the Flash as a good example of a superhero with a singleton super-power and who had to exploit it to the utmost.

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    $\begingroup$ Hmm, using this effect for miniturization has interesting ideas too! $\endgroup$ – JDługosz Oct 10 '16 at 3:46
  • $\begingroup$ @JDługosz Been there, already done that. If a volume of spacetime can be contracted, i.e., made smaller, then time will dilate. Of course, relativistic mass should increase too, so that needs hand-waving away. Glad to see you picked up on the miniaturization possibilities. $\endgroup$ – a4android Oct 10 '16 at 4:41
  • $\begingroup$ Done that: yiu mean you wrote such a story? $\endgroup$ – JDługosz Oct 10 '16 at 10:06
  • $\begingroup$ @JDługosz. Yes, this sort of miniaturization was part of it. There is plenty of scope to do lots with the idea. Could be for space travel too, assuming my reason is right. A nice simple concept really. $\endgroup$ – a4android Oct 10 '16 at 10:24
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    $\begingroup$ Just to be clear, the person inside would feel normal but the bubble would be 100,000 times larger in the outside world when switched on. It would not fit in the same place. $\endgroup$ – JDługosz Oct 10 '16 at 10:31
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To me, the biggest worry beyond those already mentioned is heat transfer. Heat energy is effectively the kinetic energy belonging to individual molecules, which is proportional to the square of the molecule's speed. Within the bubble, the average speed of a molecule is 100000x faster; the average kinetic energy is therefore magnified by a factor of $10^{10}$, or ten billion.

The human body clocks in at about $310$ Kelvin. Scaled up - and bearing in mind that we have no need to account for heat of vaporization or other phase changes - from outside the bubble the individual inside would seem to be upwards of three trillion Kelvin. For comparison, the core of the Sun is less than thirty million Kelvin, and its surface is only six thousand. Standing near a person inside such a bubble would be like standing inside a hundred thousand suns. The heat transfer would be virtually instantaneous and catastrophic. The average person is $62$ kilograms and has a specific heat of $3470$ J/kgC; three trillion Kelvin then means that the person's body contains about $6.5 \cdot 10^{17}$ Joules of energy. Transferring all that energy would amount to about the energy output of a $150$-megaton nuclear weapon, three times the power of the largest nuclear weapon ever detonated.

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It seems to me that the volume inside the bubble would quickly become near-vacuum unless the border somehow actively maintained pressure. If the air molecules outside the bubble are effectively moving 100,000 times slower than inside, then air molecules would exit the bubble 100,000 times more often than enter it. This would have the effect of making the effective "air pressure" outside the bubble 100,000 times less than inside.

If the border somehow actively exchanged air with the outside environment at a rate needed to simulate a 1 km/h breeze, outside the bubble there would be a 100,000 km/h wind. A category 5 hurricane is 251 km/h, so this would cause immense wind (and probably heat).

I suppose a solution would be to make the border impervious to air and have any molecule that comes in contact with the border simply be displaced to the opposite side. But then how does the user interact with their environment at all? A molecular whitelist?

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  • $\begingroup$ Welcome to Worldbuilding SE, Spacedog! You seem to have jumped right in with a great first post. We're glad to have you. $\endgroup$ – type_outcast Oct 11 '16 at 16:56
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Nice idea. I guess the idea comes partly from the "Bobbles" from some other book that work the other way round (stopping time inside).

You could use this if you have a difficult problem to solve => enclose yourself in the bubble with the fastest computer or whatever (and some energy source and all that), and think it through real neat. Then you can come out a second later and would have solved whatever would have taken someone else a dozen years to solve.

This throws up a problem though: you need to bring everything with you, and can't really get rid of stuff either. This means, energy (for light, or a computer or whatever you want to use), food, etc.; there is no point entering the bubble unless you want to achieve something in there.

As you say the border is a few cm think, and things can cross it - I guess you mean that the border consists solely of the time effect; no boundary otherwise, that would keep stuff in or out. This would make it absurdly complicated. If you put your hand through it, the part of your body inside would skeletify and turn to dust long before the rest would enter (without invoking any real science here; just going from the stated time effect). So you would have a way to let the bubble spring into existence around you at an instant (or at least at the same speed for the whole volume).

For comparison: said "Bobble" (from Vernor Vinge) works by enclosing a spherical volume in a metallic/shiny border; neatly slicing through everything. The border is completely impervious to anything - no tool can scratch it, no amount of energy whatsoever can influence it in any way, light reflects perfectly, etc.

Inside, time stops. At a pre-set time, the bobble disappears (in an instant) and time flows normal again. It just "works", there are no side effects. It is an absurdly neat solution to the time travel problem - at least in one direction (the correct one :) ). It is used to great storytelling effect to let people and items (rockets :-) ) skip over events in the real world. He even builds a working spaceship out of them at a later time, you can easily see how.

I believe you can make it work just like that, if you get rid of your "thick" border and replace it by an infinitely thin one that is absolute uncrossable from both sides. You don't need to explain anything (unless you want to make the technical explanation how it works a main part of your story) and get loads of material out of it. It's just a little less practical, as everything "interesting" happens inside the bubble, and thus in a very confined space. You have no outside benefit to enbubbling something (unlike the freeze-bobble).

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  • $\begingroup$ But the interesting thing is the effects at the border! That's what I'm interested in - otherwise it's merely a boring way of time travelling $\endgroup$ – Drgabble Oct 10 '16 at 13:30
  • $\begingroup$ Meta-Question: someone tagged this as "asks for hard science", it should be "backed up by equations, empirical evidence, papers, citations". I understand this, but how exactly do you expect to have a time travel related question to be backed by equations, evidence, papers, citations? If you feel my answer (that brings up several points that are logically self-evident from the frameset of the question) not to belong here, feel free to remove it. $\endgroup$ – AnoE Oct 10 '16 at 15:59
  • $\begingroup$ @Drgabble As for most questions related to time, the problem is that nobody knows what time actually is. Sure, Einstein. But he manipulates time strictly in the frameset of observers moving relatively to each other. Saying "in this area of space, time moves slower/faster" is meaningful in our current physics, so it will be very hard indeed to find any meaningful formulas which are not just mumbo jumbo. It would be easiest for you just to take a "naive" interpretation of what time means and go from there. Like said above, stick your hand in and imagine what happens. $\endgroup$ – AnoE Oct 10 '16 at 16:07
  • $\begingroup$ That should read "is not meaningful" of course. $\endgroup$ – AnoE Oct 10 '16 at 16:15
  • $\begingroup$ He downraded to science-based, so son’t worry about hard-science but kudos to celtschk who answered when it still was! $\endgroup$ – JDługosz Oct 10 '16 at 18:01
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There's a pretty damn good miniseries called The Lost Room which featured a device (The Comb) that stopped time for the user. It had some very interesting and unique rules:

  • A person using the device could not interact with anything. Everything else in the world was locked in place - he couldn't pick up anything, or open a door.
  • Momentum was preserved. If the user was running when he used The Comb, if he didn't start running again, in the same direction and speed, when time started up again, he would lurch in the direction he was travelling before its use.
  • Light behaved very strangely (everything looked washed out and gray), and there was no sound.

I always thought these were neat takes on the very often used concept.

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